Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma \mathrm{/}{f}_0(500)$ meson

We summarize recent results on studies of $\pi \pi$ and $\pi N$ scatterings. They include the finding of a negative-parity nucleon pole with a mass lower than the nucleon mass, and the pole trajectory of $f_0(500)$ as the pion mass varies. The results are obtained from model-independent dispersion analyses. We also study the thermal properties of $f_0(500)$ based on the $O(N)$ $\sigma$ model and $N\mathrm{/}D$ method.